Solution
= Solution
The <transition matrix> acts on a column <probability vector> in the order Central, Headington, Botley. Thus column $j$ records the destinations of buses starting at station $j$. The Central-to-Headington, Headington-to-Botley and Botley-to-Central entries give
$$
\boxed{A=B=C=0.1,\qquad P=\begin{pmatrix}0.6&0.1&0.1\\0.1&0.8&0.2\\0.3&0.1&0.7\end{pmatrix}.}
$$
Each column sums to one, as required for this column convention for a <stochastic matrix>.